The graph of a rational function fis shown below. Assume that all asymptotes and intercepts are shown and that the graph has no "holes". Use the graph to complete the following. (a) Write the equations for all vertical and horizontal asymptotes. Enter the equations using the "and" button as necessary. Select "None" as necessary. Vertical asymptote(s): Horizontal asymptote(s): (b) Find all x-intercepts and y-intercepts. Check all that apply. x- O -1 O-3 O-6 O None intercept(s): y- intercept(s): 口-6 O -2 O-3 口 None (c) Find the domain and range of f. Write each answer as an interval or union of intervals. Domain:| Range:
The graph of a rational function fis shown below. Assume that all asymptotes and intercepts are shown and that the graph has no "holes". Use the graph to complete the following. (a) Write the equations for all vertical and horizontal asymptotes. Enter the equations using the "and" button as necessary. Select "None" as necessary. Vertical asymptote(s): Horizontal asymptote(s): (b) Find all x-intercepts and y-intercepts. Check all that apply. x- O -1 O-3 O-6 O None intercept(s): y- intercept(s): 口-6 O -2 O-3 口 None (c) Find the domain and range of f. Write each answer as an interval or union of intervals. Domain:| Range:
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Rational Function Analysis**
The graph of a rational function \(f\) is shown below. Assume that all asymptotes and intercepts are shown and that the graph has no "holes".
Use the graph to complete the following tasks.
---
![Graph Description]
Observe the given graph. It features a rational function with distinct vertical and horizontal asymptotes. The function appears to approach the vertical asymptote at \( x = 1 \) and the horizontal asymptote at \( y = 2 \).
---
### Questions and Tasks
**(a) Write the equations for all vertical and horizontal asymptotes. Enter the equations using the "and" button as necessary. Select "None" as necessary.**
- Vertical Asymptote(s): \( x = 1 \)
- Horizontal Asymptote(s): \( y = 2 \)
**(b) Find all x-intercepts and y-intercepts. Check all that apply.**
- x-intercept(s):
- [ ] \( -1 \)
- [ ] \( -3 \)
- [ ] \( -6 \)
- [x] None
- y-intercept(s):
- [ ] \( -6 \)
- [ ] \( -2 \)
- [ ] \( -3 \)
- [x] None
**(c) Find the domain and range of \( f \). Write each answer as an interval or union of intervals.**
- Domain: \( (-\infty, 1) \cup (1, \infty) \)
- Range: \( (-\infty, 2) \cup (2, \infty) \)
---
**Graph Details**
The graph depicts two asymptotes: one vertical asymptote at \( x = 1 \) and one horizontal asymptote at \( y = 2 \). The curve of the function approaches these asymptotes but never intersects them. The function does not cross the x-axis or y-axis, indicating no real x-intercepts or y-intercepts.
Using this information, you can accurately describe the characteristics and behaviors of the rational function \( f \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7b2cf625-4036-4720-a556-8dac8a6487c8%2F8257b721-1e9b-444c-ad03-4c8882545510%2Fsy2vgwc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Rational Function Analysis**
The graph of a rational function \(f\) is shown below. Assume that all asymptotes and intercepts are shown and that the graph has no "holes".
Use the graph to complete the following tasks.
---
![Graph Description]
Observe the given graph. It features a rational function with distinct vertical and horizontal asymptotes. The function appears to approach the vertical asymptote at \( x = 1 \) and the horizontal asymptote at \( y = 2 \).
---
### Questions and Tasks
**(a) Write the equations for all vertical and horizontal asymptotes. Enter the equations using the "and" button as necessary. Select "None" as necessary.**
- Vertical Asymptote(s): \( x = 1 \)
- Horizontal Asymptote(s): \( y = 2 \)
**(b) Find all x-intercepts and y-intercepts. Check all that apply.**
- x-intercept(s):
- [ ] \( -1 \)
- [ ] \( -3 \)
- [ ] \( -6 \)
- [x] None
- y-intercept(s):
- [ ] \( -6 \)
- [ ] \( -2 \)
- [ ] \( -3 \)
- [x] None
**(c) Find the domain and range of \( f \). Write each answer as an interval or union of intervals.**
- Domain: \( (-\infty, 1) \cup (1, \infty) \)
- Range: \( (-\infty, 2) \cup (2, \infty) \)
---
**Graph Details**
The graph depicts two asymptotes: one vertical asymptote at \( x = 1 \) and one horizontal asymptote at \( y = 2 \). The curve of the function approaches these asymptotes but never intersects them. The function does not cross the x-axis or y-axis, indicating no real x-intercepts or y-intercepts.
Using this information, you can accurately describe the characteristics and behaviors of the rational function \( f \).
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